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<h1 class="reftitle">mpt_call_mplp</h1>
<h2>Purpose</h2>
<p>A gateway function to MPLP solver (without errorchecks)</p>
<h2>Syntax</h2>
<pre class="synopsis">R = mpt_call_mplp(S)</pre>
<h2>Description</h2>
<p></p>
        The function call to MPLP solver from <tt>Opt</tt> class.
        Note that this solver is not capable of solving MPLP with the parameterized cost
        function, i.e. if there is non-zero <tt>pF</tt> term.
        
        Using option settings for MPLP solver taken from MPT2.6.
	<h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>S</tt></td>
<td>
<p></p>Object of the <tt>Opt</tt> class<p>
	    		Class: <tt>Opt</tt><p></p><tr valign="top">
<td><tt>S.H</tt></td>
<td>
<p></p>Quadratic part of the objective function.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: 0</p>
</td>
</tr><tr valign="top">
<td><tt>S.f</tt></td>
<td>
<p></p>Linear part of the objective function.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.pF</tt></td>
<td>
<p></p>Linear part of the objective function for parameters.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: 0</p>
</td>
</tr><tr valign="top">
<td><tt>S.A</tt></td>
<td>
<p></p>Linear part of the inequality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp1.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp1.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.b</tt></td>
<td>
<p></p>Right hand side of the inequality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp2.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp2.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.pB</tt></td>
<td>
<p></p>Right hand side of the inequality constraints for parameters <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp3.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp3.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.Ae</tt></td>
<td>
<p></p>Linear part of the equality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp4.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp4.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.be</tt></td>
<td>
<p></p>Right hand side of the equality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp5.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp5.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.pE</tt></td>
<td>
<p></p>Right hand side of the equality constraints for parameters <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp6.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp6.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.lb</tt></td>
<td>
<p></p>Lower bound for the decision variables <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp7.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp7.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.ub</tt></td>
<td>
<p></p>Upper bound for the decision variables <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp8.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp8.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.Ath</tt></td>
<td>
<p></p>Linear part of the inequality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp9.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp9.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.bth</tt></td>
<td>
<p></p>Right hand side of the inequality constraints <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp10.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp10.png">.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.M</tt></td>
<td>
<p></p>Linear matrix involved in LCP.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.q</tt></td>
<td>
<p></p>Right hand side vector involved in LCP.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.Q</tt></td>
<td>
<p></p>Linear matrix involved in parametric formulation of LCP.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.n</tt></td>
<td>
<p></p>Number of decision variables.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.d</tt></td>
<td>
<p></p>Number of parameters.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.m</tt></td>
<td>
<p></p>Number of inequalities in <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp11.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp11.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.me</tt></td>
<td>
<p></p>Number of equalities in <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp12.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp12.png">.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr><tr valign="top">
<td><tt>S.problem_type</tt></td>
<td>
<p></p>A string specifying the problem to be solved<p>
	    		Class: <tt>char</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.varOrder</tt></td>
<td>
<p></p>Order of variables if the problem was processed by YALMIP first.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.Internal</tt></td>
<td>
<p></p>Internal property of <tt>Opt</tt> class.<p>
	    		Class: <tt>struct</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.recover</tt></td>
<td>
<p></p>Affine map for MPLP problems if there were any equalities present and have been removed by <tt>eliminateEquations</tt> method.<p>
	    		Class: <tt>struct</tt><p></p><tr valign="top">
<td><tt>S.recover.Y</tt></td>
<td>
<p></p>Matrix of the affine map <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp13.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp13.png">.
                            The map is from the optimization variables involed in the reduced MPLP <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp14.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp14.png"> to the original MPLP.
                        <p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><tr valign="top">
<td><tt>S.recover.th</tt></td>
<td>
<p></p>Matrix of the affine map <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp15.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp15.png">.
                            The map is from the optimization variables involed in the reduced MPLP <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp16.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp16.png"> to the original MPLP.
                        <p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: []</p>
</td>
</tr><p></p></p>
<p>
	    		Default: []</p>
</td>
</tr><p></p></p>
</td>
</tr></tbody>
</table>
<h2>Output Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>R</tt></td>
<td>
<p></p>result structure<p>
	    		Class: <tt>struct</tt><p></p><tr valign="top">
<td><tt>R.xopt</tt></td>
<td>
<p></p>Optimal solution<p>
	    		Class: <tt>PolyUnion</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol</tt></td>
<td>
<p></p>Structure with the solution as returned by MPLP solver.<p>
	    		Class: <tt>struct</tt><p></p><tr valign="top">
<td><tt>R.mplpsol.Pn</tt></td>
<td>
<p></p>Array of polytopes in MPT2 format. <p>
	    		Class: <tt>polytope</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol.Fi</tt></td>
<td>
<p></p>Cell array of matrices of the control law given as <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp17.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp17.png">. <p>
	    		Class: <tt>cell</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol.Gi</tt></td>
<td>
<p></p>Cell array of matrices of the control law given as <img src="../../../../fig/mpt/modules/solvers/mpt_call_mplp18.png" alt="../../../../fig/mpt/modules/solvers/mpt_call_mplp18.png">. <p>
	    		Class: <tt>cell</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol.activeConstraints</tt></td>
<td>
<p></p>Index set of active constraints<p>
	    		Class: <tt>cell</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol.Phard</tt></td>
<td>
<p></p>Feasible domain.<p>
	    		Class: <tt>polytope</tt></p>
</td>
</tr><tr valign="top">
<td><tt>R.mplpsol.details</tt></td>
<td>
<p></p>More details about the solution and the computation.<p>
	    		Class: <tt>struct</tt></p>
</td>
</tr><p></p></p>
</td>
</tr><p></p></p>
</td>
</tr></tbody>
</table>
<h2>See Also</h2>
<a href="./@Opt/opt.html">opt</a>, <a href="./mpt_solvemp.html">mpt_solvemp</a><p></p>
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<br><p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
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